Theorems · Theorem · real analysis
Complex.sin_pi_div_two_sub
∀ (x : ℂ), Complex.sin (↑Real.pi / 2 - x) = Complex.cos x
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 179 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Complexstatement and proof · cited by 5,565
- one_mulproof · cited by 2,841
- add_zeroproof · cited by 2,707
- Real.pistatement and proof · cited by 1,774
- Complex.ofRealstatement and proof · cited by 1,654
- MulZeroClass.zero_mulproof · cited by 1,625
- sub_eq_add_negproof · cited by 1,023
- mul_negproof · cited by 590
- neg_zeroproof · cited by 542
- Complex.cosstatement and proof · cited by 279
- Complex.sinstatement and proof · cited by 258
- Complex.cos_negproof · cited by 17
Cited by2
Results whose statement or proof uses this declaration.
- Complex.Gammaℝ_one_sub_mul_Gammaℝ_one_addproof · cited by 1
- Complex.tan_pi_div_two_subproof · cited by 0